Fiber optic 3D shape sensing involves localizing and quantifying deformation occurring at one or more locations along the length of a fiber-based sensor.
Such deformation may be single degree of freedom bending of a joint and require just one sensor, or, it may be a complex combination of bending, twisting, and axial elongation which varies with sensor length, thus requiring a distributed measurement.
This spectrum of requirements has resulted in a variety of 3D shape sensing approaches ranging from intensity measurements and the use of illuminating coatings to the most common technique, fiber Bragg gratings. Each of these techniques quantifies various types of deformation which is then used to interpret the shape of the fiber.
Because of the tortuous paths and complex deformations associated with medical devices such as catheters and endoscopes, The Shape Sensing Company (TSSC) has implemented a solution using distributed fiber Bragg gratings (FBGs).
This enables the TSSC technology to simultaneously measure three-dimensional bending, twisting, axial elongation and compression, and temperature changes in a spatially continuous manner along the entire sensor, enabling the highest possible accuracy in shape reconstruction. The cross section and linear configuration of a typical FBG-based 3D shape sensor is shown below in Figure 1.
Figure 1: FBG-based 3D shape sensor configuration 
The left side of Figure 1 shows a 3D sensor consisting of seven cores or individual fibers with inscribed arrays of FBG sensors, seen as the grey dashes.
With the TSSC technology the length of each FBG, l, is a few tens of microns and d, the distance between each FBG is zero microns, yielding a truly continuous measurement configuration.
The FBGs act as a distribution of strain gauges and accurately quantify and localize bending, twisting, and stretching that occurs anywhere along the sensor length.
The right side of Figure 1 shows the cross-sectional geometry. Knowledge of each cores’ location relative to the neutral axis allows one to determine the direction of bending, enabling a three-dimensional reconstruction of its shape.
Coordinates are calculated once the distribution of bending radius, R(s), bending direction, Θ(s), and twist, Φ(s), have all been determined as functions of arc length, s, from the constitutive cores’ strain distributions, ε₁₋₄(s). This progression is illustrated below by Eq. 1.
ε₁(s), ε₂(s), ε₃(s), ε₄(s) → R(s), Θ(s), Φ(s) → [ x(s), y(s), z(s) ] (Eq. 1)
The accuracy of the resulting shape relies on how well the deformation distributions are resolved.
In other words, the more information you have along the arc length of the sensor, the better the deformation is resolved, and the more accurate the constructed 3D shape will be.
Technologies which rely on intensity measurements, illuminating coatings, and coarse FBG sensors are not able to resolve these distributions with sufficient granularity to accurately reconstruct complex and tortuous paths.
It is for this reason that medical device, robotics, and inspection technology providers are turning to the solution offered by The Shape Sensing Company to enable their next generation of products. Contact us today to learn more about how 3D shape sensing measurements are performed and how the technology can help push your product development to the next level.
 Sonja Jackle, Tim Eixmann, Hinnerk Shulz-Hildebrandt, Gereon Huttmann, Torben Patz (2019) Fiber optical shape sensing of flexible instruments for endovascular navigation. International Journal of Computer Assisted Radiology and Surgery.